Filter calibration using Landolt Star

RGB imaging exposure time calibration using the Landolt Catalog

When making color images, this is important to have the three R, G and B images with the same signal to noise ratio in order to achieve well balanced images. In a simple words, you may expose the R image 600s, but what about the G and B images ? What will be the exposure time to use ? One can reply that the G and B image could be exposed the same as the Red image, but one must keep in mind that the filters do not have all the same efficiency and the CCD does not have the same Quantum efficiency over the 300 to 1100 nm range. So for instance, this is more likely that the blue frame must be more exposed than the red frame, but how ? This page explains how to calibrate the exposure time to get good set of B&W images before making the RGB image. This depends on the type of the set of filters and the CCD quantum efficiency curve.

First off all, this is the set of filter to use. This is Schott color filters, you can get the transmittance plot of each combination by clicking to it.

Blue (B)	BG12 (1 mm) + BG18 (2 mm)
Green (G)	GG495 (2 mm) + BG 18 (1 mm)
Red (R)	OG570 (2 mm) + KG3 (1 mm)

Using this set of filters is really convenient because lot of stars have been calibrated with this set of filter.

The Landolt catalog is made of selected fields spread over the celestial equator. Each field has between 5 to 20 calibrated stars per square degree. The magnitude of those star is ranging from 12 to 9. The measurements are really accurate , down to 1/1000 magnitude !

I have found and interesting field at RA=23h42m35s DEC=+01°05'36'' and selected the star called Landolt115420, looking to its brightness at different band, one can get :

	1	2	3
Band	Magnitude	Appearance	Ratio
V	11.16	-	1
B-V	0.468	Star is brighter in Green	1.53
V-R	0.286	Star is brighter in Red	1.30

Table 1: Landolt115420 star

1 : Magnitudes from the Landolt catalog
2 : Appearance or visible differences
3 : Ratios, ie 2.512^0.468 and 2.512^0.286

Chart of 2x2° containing Landolt 115420

The B,V,R band are the one defined by the set of Schott filters as defined above.

Then using the CCD E2V 47-10 (formerly Marconi) and a T250 F3.5 telescope, I could compile this table :

	1	2	3	4	5
	Flux meas. (Image)	Exp. Time	Flux Exp. Time Normalized (70s)	Flux Expected	Ratios
V	146212	70s	146212	146212	1
R	225120	70s	225120	190089	0.85
B	70260	190s	26000	95560	3.7

Table 2 : Flux measurement of Landolt115420

1 : This is the flux measured at the image level, expressed in ADU, annular photometry
2 : The exposure time of each image
3 : The blue image has the flux normalized by 70s/190s*70260, because the exposure time was different
4 : The expected flux : if V band is the reference, then R=V*1.3 (see table1), and B=V/1.53
5 : The ratio col4/col3 : this give the exposure time ratio to apply, where V is for instance 600s, R must be 510 and B is 2220 sec

This is really easy to get the final ratios (column 5, table 2), and for instance, If an exposing 600s using the V filter, I have to expose 510s with the R filter, 2220s with the B filter. If you plan to use a different CCD, you have to make these measurement again.

As last, but not least, the three RGB image can be combined and normalized so that to display the combined RGB image with the same display cuts levels for each image band, and then the real color of the sky can be seen !

Just notice the star that has a R magnitude of 13, whereas it has 16 blue magnitude. The star is really reddish.